4 papers
Four-coloring Eulerian triangulations of the torus
Marcin Brianski, Daniel Kral, Ander Lamaison +1
Hutchinson, Richter and Seymour [J. Combin. Theory Ser. B 84 (2002), 225-239] showed that every Eulerian triangulation of an orientable surface that has a sufficiently high represe…
Branch-depth is minor closure of contraction-deletion-depth
Marcin Briański, Daniel Kráľ, Kristýna Pekárková
The notion of branch-depth for matroids was introduced by DeVos, Kwon and Oum as the matroid analogue of the tree-depth of graphs. The contraction-deletion-depth, another tree-dept…
Closure property of contraction-depth of matroids
Marcin Brianski, Daniel Kral, Ander Lamaison
Contraction-depth is a matroid depth parameter analogous to tree-depth of graphs. We establish the matroid analogue of the classical graph theory result asserting that the tree…
Characterization of matrices with bounded Graver bases and depth parameters and applications to integer programming
Marcin Brianski, Martin Koutecky, Daniel Kral +2
An intensive line of research on fixed parameter tractability of integer programming is focused on exploiting the relation between the sparsity of a constraint matrix and the n…